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Modeling the dynamic properties of wood and wood-based composites is a challenging task due to naturally growing structure and moisture-dependent material properties. This paper presents the finite element modeling of plywood panels' dynamic properties. Two panels differing in thickness were analyzed: (i) 18 mm and (ii) 27 mm. The developed models consisted of individual layers of wood, which were discretized using three-dimensional finite elements formulated using an orthotropic material model. The models were subjected to an updating procedure based on experimentally determined frequency response functions. As a result of a model updating relative errors for natural frequencies obtained numerically and experimentally were not exceeding 2.0%, on average 0.7% for 18 mm thick panel and not exceeding 2.6%, on average 1.5% for 27 mm thick panel. To prove the utility of the method and at the same time to validate it, a model of a cabinet was built, which was then subjected to experimental verification. In this case, average relative differences for natural frequencies of 6.6% were obtained.
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There is a constant need to predict the dynamic properties of composite materials already at the design stage. A particularly attractive tool for achieving this goal is mesoscale finite element modeling. This paper presents the mesoscale modeling of the dynamic properties of polymer concrete. The method is based on finite element modeling and substructural identification. Substructural identification is a model updating technique based on frequency response functions. It enables the identification of model dynamic properties considering damping. The presented method is used to model the dynamic properties of a polymer concrete beam. In the first step, the mesoscale finite element model is built and then it is decoupled into substructures: a polymer matrix, aggregates, and an interfacial transition zone (ITZ). Next, the dynamic properties of the polymer matrix substructure are updated, and the model is reassembled. Then, second-stage updating takes place, which consists of determining the parameters of the aggregates and the ITZ. The use of substructural identification made it possible to determine the parameters of substructures that do not exist in an independent, isolated form like the ITZ. Moreover, it allows for determining the amount of damping that ITZ brings to the structure.
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Structural damping largely determines the dynamic properties of mechanical structures, especially those whose functioning is accompanied by time-varying loads. These loads may cause vibrations of a different nature, which adversely affects the functionality of the structure. Therefore, many studies have been carried out on vibration reduction methods over the last few years. Among them, the passive vibration damping method, wherein a suitable polymer system with appropriate viscoelastic properties is used, emerges as one of the simplest and most effective methods. In this view, a novel approach to conduct passive elimination of vibrations, consisting of covering elements of structures with low dynamic stiffness with polymeric pads, was developed. Herein, polymer covers were manufactured via fused filament fabrication technology (3D printing) and were joined to the structure by means of a press connection. Current work was focused on determining the damping properties of chosen polymeric materials, including thermoplastic elastomers (TPE). All investigated materials were characterized by means of differential scanning calorimetry (DSC), dynamic mechanical thermal analysis (DMTA), and mechanical properties (tensile test and Shore hardness). Lastly, the damping ability of pads made from different types of polymers were evaluated by means of dynamic tests.
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The paper presents the finite element modeling of the dynamic properties of a delta robot attached to a steel frame. A distinguishing feature of the proposed modeling method is the application of the Guyan reduction method in modeling of frame foundations. The frame in question was analyzed in two variants: (i) without attached robot and (ii) with attached robot. Based on the established model, the dynamic properties (i.e., natural frequencies, mode shapes, and frequency response functions) of the frame in the two variants were analyzed. The obtained results were then experimentally verified and validated. It was found that the developed model showed an average relative error for natural frequencies of 4.3% in the case of the frame and 5.6% in the case of the frame with the robot. The paper demonstrated the validity of the proposed model, allowing accurate and fast determination of robotic system dynamic properties.
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This article presents the results of finite element analyses of the influence of reaction forces on stresses and strains at the contact points of the rollers of prism supports with cylindrical surfaces of the main journals of large-sized crankshafts. The analyses of strains and stresses, as well as the depth of their occurrences, in the case of the shaft journal and support rollers were carried out using Hertz contact theory and the finite element method. These calculation results proved to be highly consistent. Additionally, they provide a basis for stating that, in the case under consideration, permanent deformations do not significantly affect the values of the measured geometrical deviations nor the profile forms of the supported main crankshaft journals.
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This article presents a multi-criteria analysis of the errors that may occur while measuring the geometric deviations of crankshafts that require multi-point support. The analysis included in the paper confirmed that the currently used conventional support method-in which the journals of large crankshafts rest on a set of fixed rigid vee-blocks-significantly limits the detectability of their geometric deviations, especially those of the main journal axes' positions. Insights for performing practical measurements, which will improve measurement procedures and increase measurement accuracy, are provided. The results are presented both graphically and as discrete amplitude spectra to make a visual, qualitative comparison, which is complemented by a quantitative assessment based on correlation analysis.
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At the stage of designing a special machine tool, it is necessary to analyze many variants of structural solutions of frames and load-bearing systems and to choose the best solution in terms of dynamic properties, in particular considering its resistance to chatter. For this reason, it is preferred to adopt a low-dimensional calculation model, which allows the user to reduce the necessary calculation time while maintaining a high accuracy. The paper presents the methodology of modeling the natural frequencies, mode shapes, and receptance functions of machine tool steel welded frames filled with strongly heterogenous polymer concrete, using low-dimensional models developed by the rigid finite elements method (RigFEM). In the presented study, a RigFEM model of a simple steel beam filled with polymer concrete and a frame composed of such beams were built. Then, the dynamic properties obtained on the basis of the developed RigFEM models were compared with the experimental results and the 1D and 3D finite element models (FEM) in terms of accuracy and dimensionality. As a result of the experimental verification, the full structural compliance of the RigFEM models (for beam and frame) was obtained, which was manifested by the agreement of the mode shapes. Additionally, experimental verification showed a high accuracy of the RigFEM models, obtaining for the beam model a relative error for natural frequencies of less than 4% and on average 2.2%, and for the frame model at a level not exceeding 11% and on average 5.5%. Comparing the RigFEM and FEM models, it was found that the RigFEM models have a slightly worse accuracy, with a dimensionality significantly reduced by 95% for the beam and 99.8% for the frame.
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The paper presents a new way to conduct passive elimination of vibrations consisting of covering elements of structures with low dynamic stiffness with polylactide (PLA). The PLA cover was created in 3D printing technology. The PLA cover was connected with the structure by means of a press connection. Appropriate arrangement of the PLA cover allows us to significantly increase the dissipation properties of the structure. The paper presents parametric analyses of the influence of the thickness of the cover and its distribution on the increase of the dissipation properties of the structure. Both analyses were carried out using finite element models (FEM). The effectiveness of the proposed method of increasing damping and the accuracy of the developed FEM models was verified by experimental studies. As a result, it has been proven that the developed FEM model of a free-free steel beam covered with polylactide enables the mapping of resonance frequencies at a level not exceeding 0.6% of relative error. Therefore, on its basis, it is possible to determine the parameters of the PLA cover. Comparing a free-free steel beam without cover with its PLA-covered counterpart, a reduction in the amplitude levels of the receptance function was achieved by up to 90%. The solution was validated for a steel frame for which a 37% decrease in the amplitude of the receptance function was obtained.
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This paper presents a method for modeling the dynamic properties of steel-polymer concrete beams, the basic structural components of machine tools, assembly lines, vibratory machines, and other structures subjected to time-varying loads during operation. The presented method of modeling steel-polymer concrete beams was developed using the finite element method. Three models of beams differing in cross-sectional dimensions showed high agreement with experimental data: relative error in the case of natural frequencies did not exceed 5% (2.2% on average), the models were characterized by the full agreement of mode shapes and high agreement of frequency response functions with the results of experimental tests. Additionally, the developed beam models supported the reliable description of complex structures, as demonstrated on a spatial frame, obtaining a relative error for natural frequencies of less than 3% (on average 1.7%). Full agreement with the mode shapes and high agreement with the frequency response functions were achieved in the analyzed frequency range.